论文标题
与特殊的Hermitian指标的紧凑复合歧管的Frölicher光谱序列
Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics
论文作者
论文摘要
在本文中，我们着重于Frölicher光谱序列的行为与歧管上特殊遗产指标的存在之间的相互作用，例如平衡，SKT或广义高卢顿。对具有强烈非努力的复杂结构的Nilmanifolds的平衡指标的研究使我们能够在第二页上提供无限平衡的歧管的无限族家族。此外，该结果在任何任意页面上都扩展到非分类。对于紧凑的广义高卢歧管的Frölicher光谱序列也获得了相似的结果。我们还发现了一个紧凑的SKT歧管，其frölicher光谱序列在第二页上不会退化，从而为Popovici的猜想提供了反例。
In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici.
